How to order fractions from least to greatest or from greatest to least - SSAT Upper Level Quantitative

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Order the following fractions from least to greatest:

$\frac{4}{9}$, $\frac{1}{4}$, $\frac{7}{12}$, $\frac{5}{6}$

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In order to compare these fractions, they all need to have the same denominator. The least common denominator for this set of fractions is .

Now, convert these fractions so that their denominators are all .

$\frac{4}{9}$=\frac{16}{36}$

$\frac{1}{4}$=\frac{9}{36}$

$\frac{7}{12}$=\frac{21}{36}$

$\frac{5}{6}$=\frac{30}{36}$

Now, place the fractions in ascending order by looking at the numerators.

Order the following fractions from least to greatest:

$\frac{1}{4}$, $\frac{3}{4}$, $\frac{3}{20}$, $\frac{2}{5}$

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Convert the fractions so that they all share the same denominator. Then, order the fractions from least to greatest by comparing their numerators.

$\frac{1}{4}$\cdot $\frac{5}{5}$=\frac{5}{20}$

$\frac{3}{20}$ stays the same.

$\frac{2}{5}$\cdot $\frac{4}{4}$=\frac{8}{20}$

$\frac{3}{4}$\cdot $\frac{5}{5}$=\frac{15}{20}$

$\frac{3}{20}$, $\frac{1}{4}$, $\frac{2}{5}$, $\frac{3}{4}$ is in order from least to greatest.

Order the following fractions from least to greatest:

$\frac{3}{4}$,$\frac{1}{2}$, $\frac{1}{8}$, $\frac{2}{5}$, $\frac{9}{10}$

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In order to compare these fractions, we need to rewrite them so they have a common denominator. The least common denominator of these fractions is , so starting from the left:

$\frac{3}{4}$=\frac{30}{40}$

$\frac{1}{2}$=\frac{20}{40}$

$\frac{1}{8}$=\frac{5}{40}$

$\frac{2}{5}$=\frac{16}{40}$

$\frac{9}{10}$=\frac{36}{40}$

Thus, the correct order from least to greatest is:

$\frac{1}{8}$, $\frac{2}{5}$, $\frac{1}{2}$, $\frac{3}{4}$, $\frac{9}{10}$

Order these fractions from least to greatest:

$\frac{7}{8}$, $\frac{1}{4}$, $\frac{5}{6}$, $\frac{5}{12}$

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To figure out the order of the fractions, they first all need to have the same denominator.

$\frac{7}{8}\rightarrow$\frac{21}{24}$

$\frac{1}{4}\rightarrow$\frac{6}{24}$

$\frac{5}{6}\rightarrow$\frac{20}{24}$

$\frac{5}{12}\rightarrow$\frac{10}{24}$

Now, order the fractions by looking at their numerators: $\frac{1}{4}$, $\frac{5}{12}$, $\frac{5}{6}$, $\frac{7}{8}$

Order the following fractions from least to greatest:

$\frac{1}{2}$, $\frac{9}{10}$, $\frac{3}{4}$, $\frac{5}{7}$

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Convert the fractions so that they all share the same denominator.

$\frac{1}{2}$\cdot $\frac{70}{70}$=\frac{70}{140}$

$\frac{3}{4}$\cdot $\frac{35}{35}$=\frac{105}{140}$

$\frac{5}{7}$\cdot $\frac{20}{20}$=\frac{100}{140}$

$\frac{9}{10}$\cdot $\frac{14}{14}$=\frac{126}{140}$

Now, look at the numerators and order them from the least to the greatest:

$\frac{1}{2}$, $\frac{5}{7}$, $\frac{3}{4}$, $\frac{9}{10}$

Order the following fractions from least to greatest:

$\frac{1}{8}$, $\frac{9}{24}$, $\frac{3}{4}$, $\frac{5}{12}$

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Convert all the fractions so that they share the same denominator, then order the numerators from least to greatest.

$\frac{1}{8}$\cdot $\frac{3}{3}$=\frac{3}{24}$

$\frac{9}{24}$ stays the same.

$\frac{3}{4}$\cdot $\frac{6}{6}$=\frac{18}{24}$

$\frac{5}{12}$\cdot $\frac{2}{2}$=\frac{10}{24}$

$\frac{1}{8}$, $\frac{9}{24}$, $\frac{5}{12}$, $\frac{3}{4}$ is the order of the fractions from least to greatest.

Order the following fractions from least to greatest:

$\frac{1}{5}$, $\frac{5}{8}$, $\frac{3}{10}$, $\frac{1}{4}$

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Convert the fractions so they all share the same denominator. Then, compare the numerators to order from least to greatest.

$\frac{1}{5}$\cdot $\frac{8}{8}$=\frac{8}{40}$

$\frac{5}{8}$\cdot $\frac{5}{5}$=\frac{25}{40}$

$\frac{3}{10}$\cdot $\frac{4}{4}$=\frac{12}{40}$

$\frac{1}{4}$\cdot $\frac{10}{10}$=\frac{10}{40}$

$\frac{1}{5}$, $\frac{1}{4}$, $\frac{3}{10}$, $\frac{5}{8}$ is the order of the fractions from least to greatest.

Order the following fractions from least to greatest:

$\frac{3}{16}$, $\frac{11}{16}$, $\frac{1}{4}$, $\frac{11}{32}$

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Convert the fractions so that they all share the same denominators. Then, compare their numerators to put them in order from least to greatest.

$\frac{3}{16}$ \cdot $\frac{2}{2}$=\frac{6}{32}$

$\frac{1}{4}$\cdot $\frac{8}{8}$=\frac{8}{32}$

$\frac{11}{32}$ stays the same.

$\frac{11}{16}$\cdot $\frac{2}{2}$=\frac{22}{32}$

$\frac{3}{16}$, $\frac{1}{4}$, $\frac{11}{32}$, $\frac{11}{16}$ is in order from least to greatest.

Order the following fractions from least to greatest:

$\frac{2}{9}$, $\frac{1}{3}$, $\frac{1}{18}$, $\frac{1}{6}$

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Convert the fractions so that they share the same denominator. Then, compare their numerators to put them in order from least to greatest.

$\frac{1}{18}$\cdot $\frac{2}{2}$=\frac{2}{36}$

$\frac{1}{6}$\cdot $\frac{6}{6}$=\frac{6}{36}$

$\frac{2}{9}$\cdot $\frac{4}{4}$=\frac{8}{36}$

$\frac{1}{3}$\cdot $\frac{12}{12}$=\frac{12}{36}$

$\frac{1}{18}$, $\frac{1}{6}$, $\frac{2}{9}$, $\frac{1}{3}$ is in order from least to greatest.

Order the following fractions from greatest to least:

$\frac{9}{10}$, $\frac{1}{5}$, $\frac{18}{25}$, $\frac{7}{20}$

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Convert the fractions so that they all share the same denominator. Then, compare their numerators to put them in order from greatest to least.

$\frac{9}{10}$\cdot $\frac{10}{10}$=\frac{90}{100}$

$\frac{18}{25}$\cdot $\frac{4}{4}$=\frac{72}{100}$

$\frac{7}{20}$\cdot $\frac{5}{5}$=\frac{35}{100}$

$\frac{1}{5}$\cdot $\frac{20}{20}$=\frac{20}{100}$

$\frac{9}{10}$, $\frac{18}{25}$, $\frac{7}{20}$, $\frac{1}{5}$ is in order from greatest to least.

Order the following fractions from least to greatest:

$\frac{1}{8}$, $\frac{8}{9}$, $\frac{1}{6}$, $\frac{35}{26}$

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Convert the fractions so that they same the same denominator. Then, compare the numerators of the fractions to put them in order from least to greatest.

$\frac{1}{8}$\cdot $\frac{9}{9}$=\frac{9}{72}$

$\frac{1}{6}$\cdot $\frac{12}{12}$=\frac{12}{72}$

$\frac{8}{9}$\cdot $\frac{8}{8}$=\frac{64}{72}$

$\frac{35}{36}$\cdot $\frac{2}{2}$=\frac{70}{72}$

$\frac{1}{8}$, $\frac{1}{6}$, $\frac{8}{9}$, $\frac{35}{36}$ is in order from least to greatest.

Order the following fractions from greatest to least:

$\frac{3}{4}$, $\frac{7}{8}$, $\frac{3}{20}$, $\frac{13}{20}$

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Convert the fractions so that they share the same denominator. Then, compare their numerators in order to put them from greatest to least.

$\frac{7}{8}$\cdot $\frac{10}{10}$=\frac{70}{80}$

$\frac{3}{4}$\cdot $\frac{20}{20}$=\frac{60}{80}$

$\frac{13}{20}$\cdot $\frac{4}{4}$=\frac{52}{80}$

$\frac{3}{20}$\cdot $\frac{4}{4}$=\frac{12}{80}$

$\frac{7}{8}$, $\frac{3}{4}$, $\frac{13}{20}$, $\frac{3}{20}$ is in order from greatest to least.

Order the following fractions from greatest to least:

$\frac{3}{10}$, $\frac{1}{5}$, $\frac{1}{25}$, $\frac{13}{25}$

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Convert the fractions so that they share the same denominator. Then, compare their numerators to order them from greatest to least.

$\frac{13}{25}$\cdot $\frac{2}{2}$=\frac{26}{50}$

$\frac{3}{10}$\cdot $\frac{5}{5}$=\frac{15}{50}$

$\frac{1}{5}$\cdot $\frac{10}{10}$=\frac{10}{50}$

$\frac{1}{25}$\cdot $\frac{2}{2}$=\frac{2}{50}$

$\frac{13}{25}$, $\frac{3}{10}$, $\frac{1}{5}$, $\frac{1}{25}$ is in order from greatest to least.

Order the following fractions from greatest to least:

$\frac{3}{4}$, $\frac{1}{12}$, $\frac{5}{24}$, $\frac{5}{6}$

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Convert the fractions so that they share the same denominator. Then, compare their numerators in order to put them from greatest to least.

$\frac{5}{6}$\cdot $\frac{4}{4}$=\frac{20}{24}$

$\frac{3}{4}$\cdot $\frac{6}{6}$=\frac{18}{24}$

$\frac{5}{24}$ stays the same.

$\frac{1}{12}$\cdot $\frac{2}{2}$=\frac{2}{24}$

$\frac{5}{6}$, $\frac{3}{4}$, $\frac{5}{24}$, $\frac{1}{12}$ is in order from greatest to least.

Order the following fractions from greatest to least:

$\frac{3}{5}$, $\frac{3}{10}$, $\frac{1}{6}$, $\frac{2}{3}$

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Convert the fractions so that they share the same denominator. Then, compare their numerators to put them in order from greatest to least.

$\frac{2}{3}$\cdot $\frac{10}{10}$=\frac{20}{30}$

$\frac{3}{5}$\cdot $\frac{6}{6}$=\frac{18}{30}$

$\frac{3}{10}$\cdot $\frac{3}{3}$=\frac{9}{30}$

$\frac{1}{6}$\cdot $\frac{5}{5}$=\frac{5}{30}$

$\frac{2}{3}$, $\frac{3}{5}$, $\frac{3}{10}$, $\frac{1}{6}$ is in order from greatest to least.

Order the following fractions from least to greatest: $\left($\frac{2}{3}$. $\frac{6}{11}$,$\frac{4}{7}\right)$

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To determine the correct order from least to greatest, convert all three fractions to a common denominator.

The least common denominator, LCD, can be determined by multiplying the three denominators together.

$3\times11\times7 = 231$

Convert the set by multiplying to the numerator by what was multiplied to the denominator to achieve the LCD.

$\left($\frac{2}{3}$. $\frac{6}{11}$,$\frac{4}{7}$ \right )= \left( $\frac{154}{231}$,$\frac{126}{231}$,$\frac{132}{231}\right)$

Reorder the set. The correct order from least to greatest is:

$\left( $\frac{126}{231}$,$\frac{132}{231}$,$\frac{154}{231}\right ) =\left( $\frac{6}{11}$,$\frac{4}{7}$,$\frac{2}{3}\right )$

Select the symbol to correctly fill in the blank below.

$\frac{1}{2}$ $\frac{1}{8}$

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To compare fractions, we need to first make common denominators.

$\frac{1}{2}$\times$\frac{4}{4}$=\frac{4}{8}$

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value.

$\frac{4}{8}$>$\frac{1}{8}$

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$\frac{3}{4}$ $\frac{7}{8}$

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To compare fractions, we need to first make common denominators.

$\frac{3}{4}$\times$\frac{2}{2}$=\frac{6}{8}$

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value.

$\frac{6}{8}$<$\frac{7}{8}$

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$\frac{1}{2}$ $\frac{6}{12}$

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To compare fractions, we need to first make common denominators.

$\frac{1}{2}$\times$\frac{6}{6}$=\frac{6}{12}$

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value.

$\frac{6}{12}$=\frac{6}{12}$

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$\frac{5}{7}$ $\frac{1}{3}$

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To compare fractions, we need to first make common denominators.

$\frac{5}{7}$\times$\frac{3}{3}$=\frac{15}{21}$

$\frac{1}{3}$\times$\frac{7}{7}$=\frac{7}{21}$

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value.

$\frac{15}{21}$>$\frac{7}{21}$